Basic properties
Modulus: | \(2667\) | |
Conductor: | \(2667\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(126\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2667.ei
\(\chi_{2667}(101,\cdot)\) \(\chi_{2667}(110,\cdot)\) \(\chi_{2667}(236,\cdot)\) \(\chi_{2667}(299,\cdot)\) \(\chi_{2667}(311,\cdot)\) \(\chi_{2667}(395,\cdot)\) \(\chi_{2667}(437,\cdot)\) \(\chi_{2667}(467,\cdot)\) \(\chi_{2667}(551,\cdot)\) \(\chi_{2667}(593,\cdot)\) \(\chi_{2667}(605,\cdot)\) \(\chi_{2667}(614,\cdot)\) \(\chi_{2667}(647,\cdot)\) \(\chi_{2667}(731,\cdot)\) \(\chi_{2667}(845,\cdot)\) \(\chi_{2667}(1055,\cdot)\) \(\chi_{2667}(1130,\cdot)\) \(\chi_{2667}(1235,\cdot)\) \(\chi_{2667}(1277,\cdot)\) \(\chi_{2667}(1328,\cdot)\) \(\chi_{2667}(1382,\cdot)\) \(\chi_{2667}(1403,\cdot)\) \(\chi_{2667}(1445,\cdot)\) \(\chi_{2667}(1475,\cdot)\) \(\chi_{2667}(1697,\cdot)\) \(\chi_{2667}(1706,\cdot)\) \(\chi_{2667}(1718,\cdot)\) \(\chi_{2667}(1769,\cdot)\) \(\chi_{2667}(1781,\cdot)\) \(\chi_{2667}(1928,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{63})$ |
Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((890,1144,2416)\) → \((-1,e\left(\frac{1}{6}\right),e\left(\frac{31}{126}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 2667 }(1130, a) \) | \(-1\) | \(1\) | \(e\left(\frac{23}{42}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{31}{42}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{113}{126}\right)\) | \(e\left(\frac{79}{126}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{1}{63}\right)\) | \(-1\) |